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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="compts_1.html#V6">compact</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>



<b>assume </b><a NAME="E1:144"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="pscomp_1.html#K25" target="_self">E-most</a> <font color="Maroon">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">p</font> = <font color="Maroon">x</font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> ;<br/>
<a NAME="E3:144"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E4:144"/>
( <font color="Maroon">p</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K21">`1</a>  &amp; <span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  &amp; <font color="Maroon">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">X</font></span>)</span> <a href="euclid.html#K22">`2</a>  )
 
<b>by </b><i><a class="txt" href="pscomp_1.html#E23"><i><font color="Green">Lemma103</font></i></a>, </i>;<br/>
<b>hence </b><a NAME="E5:144"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K32" target="_self">E-min</a> <font color="Maroon">X</font></span>)</span>,<span class="p1">(<span class="default"><a href="pscomp_1.html#K31" target="_self">E-max</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="pscomp_1.html#T15" target="_self">Th15</a>, <a class="ref" href="goboard7.html#T8">GOBOARD7:8</a></i>;<br/>


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